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Paper detail

Non-Holomorphic Ramanujan-type Congruences for Hurwitz Class Numbers

In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on non-holomorphic generating series. We establish a divisibility result for such non-holomorphic congruences of Hurwitz class numbers. The two keys tools in our proof are the holomorphic projection of products of theta series with a Hurwitz class number generating series and a theorem by Serre, which allows us to rule out certain congruences.

preprint2020arXivOpen access
Olivia BeckwithMartin RaumOlav K. Richter
math.NT
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Olivia BeckwithMartin RaumOlav K. Richter

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